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arXiv:2309.00601 · Physical Review A

Fast quantum gates based on Landau-Zener-Stückelberg-Majorana transitions

Joan J. Cáceres, Daniel Domı́nguez, María José Sánchez

Published Nov 29, 2023• 11 citations
arXivHTMLPDF

Abstract

Fast quantum gates are of paramount importance for enabling efficient and error-resilient quantum computations. In the present work we analyze Landau-Zener-St\"uckelberg-Majorana (LZSM) strong driving protocols, tailored to implement fast gates with particular emphasis on small-gap qubits. We derive analytical equations to determine the specific set of driving parameters for the implementation of single-qubit and two-qubit gates employing single-period sinusoidal pulses. Our approach circumvents the need to scan experimentally a wide range of parameters and instead it allows to concentrate on fine-tuning the device near the analytically predicted values. We analyze the dependence of relaxation and decoherence on the amplitude and frequency of the pulses, obtaining the optimal regime of driving parameters to mitigate the effects of the environment. Our study focus on the single-qubit ${X}_{\frac{\ensuremath{\pi}}{2}}, {Y}_{\frac{\ensuremath{\pi}}{2}}$ and identity gates. Also, we propose the $\sqrt{\mathrm{bSWAP}}$ as the simplest two-qubit gate attainable through a robust LZSM driving protocol.

DOI
10.1103/physreva.108.052619

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Fast quantum gates are of paramount importance for enabling efficient and error-resilient quantum computations. In the present work we analyze Landau-Zener-St"uckelberg-Majorana (LZSM) strong driving protocols, tailored to implement fast gates with particular emphasis on small-gap qubits. We derive analytical equations to determine the specific set of driving parameters for the implementation of single-qubit and two-qubit gates employing single-period sinusoidal pulses. Our approach circumvents the need to scan experimentally a wide range of parameters and instead it allows to concentrate on fine-tuning the device near the analytically predicted values. We analyze the dependence of relaxation and decoherence on the amplitude and frequency of the pulses, obtaining the optimal regime of driving parameters to mitigate the effects of the environment. Our study focus on the single-qubit X\ensuremathπ2,Y\ensuremathπ2{X}_{\frac{\ensuremath{\pi}}{2}}, {Y}_{\frac{\ensuremath{\pi}}{2}}X2\ensuremathπ​​,Y2\ensuremathπ​​ and identity gates. Also, we propose the bSWAP\sqrt{\mathrm{bSWAP}}bSWAP​ as the simplest two-qubit gate attainable through a robust LZSM driving protocol.
Quantum gates based on resonant Rabi oscillations are inherently slow for small-frequency qubits. They are also prone to errors due to counter-rotating terms. However, when the anharmonicity is sufficiently high, as in the fluxonium architecture, alternative manipulation protocols can outperform standard resonant driving. In this work, we implement fast, high-fidelity quantum gates based on a one-period Landau-Zener-Stückelberg-Majorana (LZSM) driving protocol. We derive analytical expressions that simplify the exploration of the parameter space while accounting for the multi-level structure of the circuit. Furthermore, we analyze the role of leakage, discussing strategies to mitigate it and identifying regimes in which it becomes the dominant source of error. Finally, to evaluate the impact of dissipation on gate fidelity, we develop a robust formalism suitable for analyzing the open-system performance of quantum gates in the strong driving regime.
A conventional realization of quantum logic gates and control is based on resonant Rabi oscillations of the occupation probability of the system. This approach has certain limitations and complications, like counter-rotating terms. We study an alternative paradigm for implementing quantum logic gates based on Landau-Zener-Stückelberg-Majorana (LZSM) interferometry with nonresonant driving and the alternation of adiabatic evolution and nonadiabatic transitions. Compared to Rabi oscillations, the main differences are a nonresonant driving frequency and a small number of periods in the external driving. We explore the dynamics of a multilevel quantum system under LZSM drives and optimize the parameters for increasing the gate speed. We define the parameters of the external driving required for implementing a specific quantum logic gate using the adiabatic-impulse model. In particular, we demonstrate the implementations of single-qubit X, Y, Hadamard gates, and two-qubit i and gates using the LZSM transitions. The considered LZSM approach for implementing arbitrary quantum logic gates can be applied to a large variety of multilevel quantum systems and external driving. Published by the American Physical Society 2024
Achieving very fast gates that undercut the natural limits set by decoherence requires going into the strong driving limit. Realizing single-qubit control predicted beyond semi-classical, time-dependent modeling has yet to be experimentally realized on superconducting and most other computing platforms. In this regime, the common model of dynamics within a three-level manifold breaks down, and instead, we see new quantum error channels growing abruptly with decreasing time. To identify these error processes we systematically calculate the effect of multi-photon transitions that occur out of the computational space. We then derive analytical formulas to suppress these effects, as well as amplitude and phase errors on the qubit space; we term these R1D for suppressing the ∣0⟩−∣2⟩|0\rangle-|2\rangle∣0⟩−∣2⟩ transition and R2D when also suppressing ∣1⟩−∣3⟩|1\rangle-|3\rangle∣1⟩−∣3⟩ leakage. We also answer long-standing questions about the optimal values of the DRAG prefactor as well as constant detuning, when accounting for time-ordering, and also show how to calibrate other prefactors for further performance improvement. Upon correcting these varied sources of error, we numerically demonstrate gate infidelities below 10−510^{-5}10−5 for a 7ns πππ-rotation when incorporating existing decoherence rates.
Constructing a universal operation scheme for Majorana qubits remains a central issue for the topological quantum computation. We study the Landau-Zener-St\"uckelberg interference in a Majorana qubit and show that this interference can be used to achieve controllable operations. The Majorana qubit consists of an rf superconducting quantum interference device (SQUID) with a topological nanowire Josephson junction which hosts Majorana bound states. In the SQUID, a magnetic flux pulse can drive the quantum evolution of the Majorana qubit. The qubit experiences two Landau-Zener transitions when the amplitude of the pulse is tuned around the superconducting flux quanta h/2eh/2eh/2e. The Landau-Zener-St\"uckelberg interference between the two transitions rotates the Majorana qubit, with the angle controlled by the time scale of the pulse. This rotation operation implements a high-speed single-qubit gate on the Majorana qubit, which is a necessary ingredient for the topological quantum computation.
We investigate an analogy between quantum signal processing (QSP) and the adiabatic-impulse model (AIM) in order to implement the QSP algorithm with fast quantum logic gates. QSP is an algorithmic technique that uses single-qubit dynamics to perform a polynomial function transformation. The adiabatic-impulse model effectively describes the evolution of a two-level quantum system under a strong external driving field. We can map parameters from QSP to the AIM to implement a QSP-like evolution with nonadiabatic, high-amplitude external drives. By choosing the AIM driving parameters that control the nonadiabatic transition parameters (such as driving amplitude A , frequency ω , and signal timing), one can achieve polynomial approximations and increase robustness in quantum circuits. The analogy between QSP and AIM presented here can be useful as a way to directly implement the QSP algorithmic technique on quantum systems and show the benefits from fast Landau-Zener-Stückelberg-Majorana (LZSM) quantum logic gates in comparison with usual resonance driving gates in IBM-Q quantum processors.
A register of quantum bits with fixed transition frequencies and weakly coupled to one another through simple linear circuit elements is an experimentally minimal architecture for a small-scale superconducting quantum information processor. Presently, the known schemes for implementing two-qubit gates in this system require microwave signals having amplitudes and frequencies precisely tuned to meet a resonance condition, leaving only the signal phases as free experimentally adjustable parameters. Here, we report a minimal and robust microwave scheme to generate fast, tunable universal two-qubit gates: simply irradiate one qubit (the ``control'') at the transition frequency of another (the ``target''). The effective coupling between them is then switched on by tuning only the frequency of this single drive tone; the drive amplitude adjusts the effective coupling strength; and the drive phase selects the particular two-qubit gate implemented. This cross-resonance effect turns on linearly with the ratio of the drive amplitude $\ensuremath{\Omega}$ to the qubit-qubit detuning $\ensuremath{\Delta}$, as compared with earlier proposals that turn on as ${(\ensuremath{\Omega}/\ensuremath{\Delta})}^{4}$.